How many solutions does sin(x) = 0.01 have in the interval [0, 2π]?

To find the number of solutions for the equation sin(x) = 0.01 in the interval [0, 2π], we need to analyze the sine function.

The sine function, sin(x), oscillates between -1 and 1. For any value between -1 and 1, there will typically be two solutions within one full period of sine (which is 2π). Since 0.01 is between -1 and 1, we can conclude that there will be two solutions in the interval from 0 to 2π.

More specifically, we can find the two angles:

1. First Quadrant: x = arcsin(0.01)
2. Second Quadrant: x = π – arcsin(0.01)

Therefore, the equation sin(x) = 0.01 has two solutions in the interval [0, 2π].